Details: In one dimmer switch box I have one 14 gauge wire [with the white wire as the power supply, the black wire coming from the light fixture, and the bare ground wire]. And I have a second 14 gauge wire in that same switch box that runs over to another dimmer (which operates a separate light). I'm trying to give power to both dimmer switches from the white power wire coming in, while having both separate dimmer switches in separate locations turn on their own lights separately. I'm wondering if I need to cap off the neutral wire coming into the switch box from the other dimmer, so the lights will turn on and off their lights separately?

Tie all neutrals together. All grounds together.